Finite Group Databasebeta

← #72320879

Subgroups — #72320879

Order 1024.

2424 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#33675C211yesmaximal, characteristic
2#6345152C211yesmaximal, characteristic, complemented
3#6345074C211yesmaximal, characteristic, complemented
4#484053C218yesmaximal, complemented
5#484047C218yesmaximal, complemented
6#483841C212yesmaximal, complemented
7#483813C212yesmaximal, complemented
8#483811C212yesmaximal, complemented
9#483596C212yesmaximal, complemented
10#483420C211yesmaximal, characteristic, complemented
11#481345C211yesmaximal, characteristic, complemented
12#481065C211yesmaximal, characteristic, complemented
13#479963C211yesmaximal, characteristic, complemented
14C2×#3169C2211yescharacteristic
15#60282—21no—
16#60236—21no—
17C2×C4×#135C2211yescharacteristic
18#33675C414yes—
19#33675C414yes—
20#33675C2214yes—
21#33675C2214yes—
22C2×#2234C412yes—
23C2×#2225C411yescharacteristic
24C2×#2224C411yescharacteristic
25C2×#2207C411yescharacteristic
26C2×#2206C411yescharacteristic
27C2×#2186C412yes—
28C2×#2177C2212yes—
29C2×#2175C2212yes—
30C2×#2163C2211yescharacteristic
31C2×C4×M32C2211yescharacteristic
32#18091C2214yescomplemented
33#18084—22no—
34#18073C2214yescomplemented
35#18066—22no—
36#18065C2214yescomplemented
37#18055—22no—
38#18045C2214yescomplemented
39#18035—22no—
40#17897C2212yes—
41#17895C2212yes—
42#17879—22no—
43#17877—22no—
44#17854C2212yes—
45#17854C2212yes—
46#17793C2211yescharacteristic
47C2×#1564C2211yescharacteristic
48#17463—21no—
49#17450—21no—
50#17323C2211yescharacteristic
51#12087C22116yescomplemented
52#12078C22116yescomplemented
53#12077C22116yescomplemented
54#12067C22116yescomplemented
55#12031C2214yescomplemented
56#12030C2214yescomplemented
57#11999C2212yes—
58#11999C2212yes—
59#11680C2214yescomplemented
60#11678C2214yescomplemented
61#11600C2211yescharacteristic
62#11600C2211yescharacteristic
63#11599C2212yes—
64#11599C2211yescharacteristic
65#11599C2211yescharacteristic
66#11599C2212yes—
67#11598C2214yescomplemented
68#11597C2214yescomplemented
69#11414C2214yescomplemented
70#11413C2214yescomplemented
71#11406C2212yes—
72#11405C2212yes—
73C22×#135C2×C411yescharacteristic
74C2×#532—21no—
75C2×C4×#41—21no—
76C22×SD32C2×C412yes—
77C22×D16C2×C412yes—
78C22×M32—21no—
79#3169—21no—
80#3169—21no—
81#3169—21no—
82#3169—21no—
83#3169C2×C412yes—
84#3169C2×C412yes—
85#3169C2312yes—
86#3169C2312yes—
87C2×#500C2×C411yescharacteristic
88C2×#493C2×C411yescharacteristic
89C2×#486—21no—
90C2×#466—21no—
91C2×#466C2×C412yes—
92#2990—24no—
93#2990—42no—
94#2983—22no—
95#2981—42no—
96#2979—24no—
97#2975—22no—
98#2974—42no—
99#2973—42no—
100#2972—22no—
101#2972—22no—
102#2970—24no—
103#2970—42no—
104C4×#135—21no—
105C4×#135—21no—
106C4×#135—21no—
107C4×#135—21no—
108C4×#135C2×C412yes—
109C4×#135C2×C412yes—
110C4×#135C2312yes—
111C4×#135C2312yes—
112C2×C4×Q16C2×C411yescharacteristic
113C2×C4×Q16C2311yescharacteristic
114C2×C4×SD16—21no—
115C2×C4×SD16—21no—
116C2×C4×D8—21no—
117C2×C4×D8C2×C411yescharacteristic
118C2×C4×D8C2312yes—
119C2×C4×D8C2311yescharacteristic
120#2935—24no—
121#2931—42no—
122#2920—21no—
123#2920D411yescharacteristic
124#2920D411yescharacteristic
125C2×#432—42no—
126C2×#431—21no—
127C2×#427C2×C411yescharacteristic
128C2×#416—21no—
129#2880—42no—
130C22×C4×C8C2311yescharacteristic
131#2234C2×C418yes—
132#2234C2×C418yes—
133#2225C2×C414yes—
134#2225C2×C414yes—
135#2224C2×C414yes—
136#2224C2×C414yes—
137#2207C2×C414yes—
138#2207C2×C414yes—
139#2206C2×C414yes—
140#2206C2×C414yes—
141#2186C2×C418yes—
142#2186C2×C418yes—
143#2177C2×C418yes—
144#2177C2318yes—
145#2175C2×C418yes—
146#2175C2318yes—
147#2163C2×C412yes—
148#2163C2×C412yes—
149#2163C2312yes—
150#2163C2312yes—
151C2×#367C2×C412yes—
152C2×#366C2×C412yes—
153C2×C4⋊C16C2×C411yescharacteristic
154C2×C4⋊C16C2×C411yescharacteristic
155C2×#358C2×C412yes—
156C2×#357C2×C412yes—
157C2×#357C2×C412yes—
158C2×#357C2×C412yes—
159C2×C22⋊C16C2×C412yes—
160C4×M32—21no—
161C4×M32—21no—
162C4×M32C2312yes—
163C4×M32C2311yescharacteristic
164C4×M32C2311yescharacteristic
165C2×#346C2312yes—
166C2×#346C2312yes—
167C2×C4×C16—21no—
168#1594C2318yes—
169#1593C2318yes—
170#1591—24no—
171#1589—24no—
172#1586—28no—
173#1585—28no—
174#1582—28no—
175#1581—28no—
176#1580C2318yes—
177#1580C2318yes—
178C8×D8—24no—
179C8×D8—24no—
180#1568—21no—
181#1568C2312yes—
182#1567—21no—
183#1566C2312yes—
184#1564—21no—
185#1564—21no—
186#1564—21no—
187#1564C2312yes—
188#1564C2312yes—
189#1564C2311yescharacteristic
190#1564C2311yescharacteristic
191C2×#335—21no—
192C2×#334C2312yes—
193#1489—24no—
194#1488—24no—
195#1484—24no—
196#1480—24no—
197#1479—22no—
198#1478—22no—
199#1478—22no—
200#1478—22no—
201#1452D412yes—
202#1451C2312yes—
203#1451C2312yes—
204#1450C2312yes—
205C8×M16D412yes—
206C8×M16D412yes—
207#1368C2318yes—
208#1368C2318yes—
209#1334C2314yes—
210#1334C2314yes—
211#1333C2314yes—
212#1333C2318yes—
213#1333C2318yes—
214#1333C2314yes—
215#1313C2318yes—
216#1313C2318yes—
217C22×#41—21no—
218C22×#41—41no—
219C2×#135—24no—
220C2×#135—21no—
221C2×#135—21no—
222C2×#135—42no—
223C2×#135C22×C412yes—
224C2×#135C22×C412yes—
225C22×Q16C22×C411yescharacteristic
226C22×SD16—21no—
227C22×D8—21no—
228C22×D8C22×C412yes—
229C22×D8C22×C411yescharacteristic
230C2×#131—44no—
231C23×C8C22×C411yescharacteristic
232C23×C8#4111yescharacteristic
233#532—22no—
234#532—22no—
235#532—22no—
236#532—22no—
237#532—41no—
238#532—41no—
239#532—41no—
240#532—41no—
241C2×C4⋊Q8—21no—
242C2×#127—21no—
243C2×#124—41no—
244C2×#121—22no—
245C2×#121—41no—
246C4×#41—22no—
247C4×#41—22no—
248C4×#41—22no—
249C4×#41—22no—
250C4×#41—41no—
251C4×#41—41no—
252C4×#41—41no—
253C4×#41—41no—
254C2×C4×Q8—21no—
255C2×C4×Q8—21no—
256C2×C4×D4—21no—
257C2×C4×D4—21no—
258C2×C4×D4—22no—
259C2×C4×D4—41no—
260C2×C4×D4—41no—
261C2×C4×D4—41no—
262C2×#117—21no—
263C2×#117—41no—
264C22×C42—41no—
265C22×C42C2×D411yescharacteristic
266C2×SD32—44no—
267C2×SD32C22×C418yes—
268C2×D16—28no—
269C2×D16C22×C418yes—
270C2×M32—21no—
271C2×M32—22no—
272C2×M32—21no—
273C2×M32—44no—
274C22×C16—22no—
275C22×C16C22×C412yes—
276C22×C16C22×C412yes—
277#500—21no—
278#500—21no—
279#500C22×C412yes—
280#500C22×C412yes—
281#493—21no—
282#493—21no—
283#493C22×C412yes—
284#493C22×C412yes—
285#486—22no—
286#486—22no—
287#486—22no—
288#486—22no—
289#466—22no—
290#466—22no—
291#466—22no—
292#466—22no—
293#466—22no—
294#466—22no—
295#466C22×C414yes—
296#466C22×C414yes—
297#446—28no—
298#446—44no—
299C4×Q16—21no—
300C4×Q16—21no—
301C4×Q16—21no—
302C4×Q16—21no—
303C4×Q16C22×C412yes—
304C4×Q16C22×C412yes—
305C4×Q16C22×C412yes—
306C4×Q16C2412yes—
307C4×SD16—22no—
308C4×SD16—22no—
309C4×SD16—22no—
310C4×SD16—22no—
311C4×SD16—22no—
312C4×SD16—22no—
313C4×SD16—22no—
314C4×SD16—22no—
315C4×D8—22no—
316C4×D8—22no—
317C4×D8—21no—
318C4×D8—21no—
319C4×D8—21no—
320C4×D8—22no—
321C4×D8—22no—
322C4×D8—22no—
323C4×D8—22no—
324C4×D8—21no—
325C4×D8C22×C414yes—
326C4×D8C22×C412yes—
327C4×D8C22×C412yes—
328C4×D8C22×C412yes—
329C4×D8C2412yes—
330C4×D8C2414yes—
331#436—28no—
332#436—44no—
333#436—44no—
334#435—48no—
335#435—48no—
336#435—48no—
337C8×D4—28no—
338C8×D4—28no—
339C8×D4—44no—
340C8×D4—44no—
341C8×D4—44no—
342#432—21no—
343#432—21no—
344#432—21no—
345#432—21no—
346#432—22no—
347#432—44no—
348#432—44no—
349#432—44no—
350#432—41no—
351#431—21no—
352#431—21no—
353#431—22no—
354#431—22no—
355#431—41no—
356#431—41no—
357#431—41no—
358#431C2×D412yes—
359#431C2×D412yes—
360#431C2×D412yes—
361#431C2×D412yes—
362#427—21no—
363#427—21no—
364#427C22×C412yes—
365#427C22×C412yes—
366C2×#107—21no—
367C2×#107C22×C412yes—
368C2×#107C22×C411yescharacteristic
369C2×#107C22×C411yescharacteristic
370C2×#106—21no—
371#423—21no—
372#423—21no—
373#423—22no—
374C2×C4⋊C8—22no—
375C2×C4⋊C8—44no—
376#416—22no—
377#416—22no—
378#416—22no—
379#416—22no—
380C2×#103—21no—
381C2×#103—21no—
382C2×#102—22no—
383C2×#102—21no—
384C2×#102—22no—
385C2×#102—21no—
386#408—48no—
387#408—44no—
388#407—21no—
389#407—21no—
390#407—44no—
391#407—41no—
392C2×C22⋊C8—44no—
393C2×C22⋊C8—44no—
394C2×C22⋊C8—41no—
395C4×M16—41no—
396C4×M16C2×D412yes—
397C4×M16C2×D412yes—
398C2×#97—44no—
399C2×C4×C8—41no—
400C2×C4×C8C22×C411yescharacteristic
401C2×C4×C8C22×C411yescharacteristic
402C2×C4×C8C22×C411yescharacteristic
403C2×C4×C8C2×D411yescharacteristic
404C2×C4×C8C2×D411yescharacteristic
405C2×C4×C8C2×D411yescharacteristic
406C2×C4×C8#4111yescharacteristic
407C2×C4×C8#4111yescharacteristic
408C2×C4×C8#4111yescharacteristic
409C2×C4×C8C2411yescharacteristic
410C2×C4×C8C2411yescharacteristic
411C2×C4×C8C2411yescharacteristic
412#367C22×C418yes—
413#366C22×C418yes—
414C4⋊C16C22×C412yes—
415C4⋊C16C22×C412yes—
416C4⋊C16C22×C412yes—
417C4⋊C16C22×C412yes—
418#358C22×C418yes—
419#357C22×C418yes—
420#357C22×C418yes—
421#357C22×C418yes—
422C22⋊C16C22×C414yes—
423C22⋊C16C22×C414yes—
424#346—22no—
425#346C22×C414yes—
426#346C2412yes—
427#346C2412yes—
428#346C2414yes—
429C4×C16—21no—
430C4×C16—21no—
431C4×C16—22no—
432#335—21no—
433#335—22no—
434#335—21no—
435#335—22no—
436#335—22no—
437#334—22no—
438#334—22no—
439#334C2412yes—
440#334C2412yes—
441#334C2414yes—
442Q8⋊C8—28no—
443D4⋊C8—28no—
444D4⋊C8—28no—
445D4⋊C8—28no—
446#322C2×D414yes—
447#322C2×D414yes—
448#322C2414yes—
449C82C2×D414yes—
450C2×#41—22no—
451C2×#41—22no—
452C2×#41—44no—
453C2×#41—42no—
454C2×#41—42no—
455C2×#41—41no—
456C2×#41—41no—
457C2×#41—42no—
458C2×#41—42no—
459C2×#41—82no—
460C2×#41—164no—
461C22×Q8—21no—
462C22×Q8—41no—
463C22×D4—21no—
464C22×D4—22no—
465C22×D4—41no—
466C22×D4—42no—
467C22×D4—41no—
468C22×D4—41no—
469C23×C4—41no—
470C23×C4—42no—
471C23×C4—41no—
472C23×C4—41no—
473C23×C4C4×D411yescharacteristic
474C23×C4AGL(1,ℤ/8)11yescharacteristic
475C23×C4AGL(1,ℤ/8)11yescharacteristic
476#135—24no—
477#135—24no—
478#135—42no—
479#135—42no—
480#135—44no—
481#135—44no—
482C2×Q16—21no—
483C2×Q16—22no—
484C2×Q16—22no—
485C2×Q16C23×C412yes—
486C2×SD16—22no—
487C2×SD16—22no—
488C2×SD16—44no—
489C2×D8—21no—
490C2×D8—22no—
491C2×D8—22no—
492C2×D8—22no—
493C2×D8—24no—
494C2×D8—22no—
495C2×D8—24no—
496C2×D8—82no—
497C2×D8#13114yescomplemented
498C2×D8C23×C414yes—
499C2×D8C23×C412yes—
500#131—168no—
501C2×M16—22no—
502C2×M16—22no—
503C2×M16—48no—
504C2×M16—42no—
505C22×C8—22no—
506C22×C8—22no—
507C22×C8—42no—
508C22×C8—48no—
509C22×C8—48no—
510C22×C8—42no—
511C22×C8C4×D411yescharacteristic
512C22×C8C4×D411yescharacteristic
513C22×C8C4×D411yescharacteristic
514C22×C8C4×D411yescharacteristic
515C22×C8C4×D411yescharacteristic
516C22×C8C4×D411yescharacteristic
517C22×C8C23×C411yescharacteristic
518C22×C8C23×C411yescharacteristic
519C22×C8C23×C411yescharacteristic
520C22×C8C2×#4111yescharacteristic
521C22×C8C2×#4111yescharacteristic
522C22×C8C2×#4111yescharacteristic
523C4⋊Q8—22no—
524C4⋊Q8—22no—
525C4⋊Q8—41no—
526C4⋊Q8—41no—
527#127—22no—
528#127—22no—
529#127—41no—
530#127—41no—
531#124—42no—
532#124—42no—
533#124—42no—
534#124—42no—
535#121—24no—
536#121—24no—
537#121—42no—
538#121—42no—
539#121—42no—
540#121—42no—
541#121—42no—
542#121—42no—
543C4×Q8—22no—
544C4×Q8—22no—
545C4×Q8—22no—
546C4×Q8—22no—
547C4×Q8—41no—
548C4×Q8—41no—
549C4×Q8—41no—
550C4×Q8—41no—
551C4×D4—22no—
552C4×D4—22no—
553C4×D4—22no—
554C4×D4—24no—
555C4×D4—22no—
556C4×D4—24no—
557C4×D4—42no—
558C4×D4—42no—
559C4×D4—42no—
560C4×D4—42no—
561C4×D4—42no—
562C4×D4—42no—
563C4×D4—42no—
564C4×D4—42no—
565C4×D4—41no—
566C4×D4—41no—
567C4×D4—42no—
568C4×D4—42no—
569C4×D4—42no—
570C4×D4—42no—
571C4×D4—41no—
572C4×D4—41no—
573C4×D4—42no—
574C4×D4—42no—
575#117—22no—
576#117—22no—
577#117—41no—
578#117—41no—
579#117—42no—
580#117—42no—
581#117—42no—
582#117—42no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—22no—
586C2×C4⋊C4—41no—
587C2×C4⋊C4—41no—
588C2×C4⋊C4—41no—
589C2×C22⋊C4—41no—
590C2×C22⋊C4—41no—
591C2×C22⋊C4—42no—
592C2×C22⋊C4—41no—
593C2×C22⋊C4—42no—
594C2×C42—41no—
595C2×C42—41no—
596C2×C42—41no—
597C2×C42—42no—
598C2×C42—42no—
599C2×C42—42no—
600C2×C42—42no—
601C2×C42C4×D411yescharacteristic
602C2×C42C4×D411yescharacteristic
603C2×C42C4×D411yescharacteristic
604C2×C42AGL(1,ℤ/8)11yescharacteristic
605C2×C42AGL(1,ℤ/8)11yescharacteristic
606C2×C42AGL(1,ℤ/8)11yescharacteristic
607C2×C42AGL(1,ℤ/8)11yescharacteristic
608C2×C42AGL(1,ℤ/8)11yescharacteristic
609C2×C42AGL(1,ℤ/8)11yescharacteristic
610C2×C42C22×D411yescharacteristic
611C2×C42C22×D411yescharacteristic
612C2×C42C22×D411yescharacteristic
613SD32—48no—
614D16—216no—
615M32—24no—
616M32—44no—
617M32—42no—
618C2×C16—24no—
619C2×C16—24no—
620C2×C16—22no—
621C2×C16—22no—
622C2×C16—44no—
623C2×C16C23×C414yes—
624C2×C16C23×C414yes—
625#107—22no—
626#107—22no—
627#107—21no—
628#107—21no—
629#107—22no—
630#107C23×C412yes—
631#107C23×C412yes—
632#107C23×C414yes—
633#106—22no—
634#106—22no—
635C4⋊C8—22no—
636C4⋊C8—22no—
637C4⋊C8—22no—
638C4⋊C8—22no—
639C4⋊C8—22no—
640C4⋊C8—22no—
641C4⋊C8—24no—
642C4⋊C8—48no—
643C4⋊C8—42no—
644C4⋊C8—42no—
645#103—22no—
646#103—22no—
647#103—22no—
648#103—22no—
649#102—22no—
650#102—22no—
651#102—22no—
652#102—24no—
653#102—24no—
654#102—24no—
655#102—22no—
656#102—24no—
657C22⋊C8—22no—
658C22⋊C8—22no—
659C22⋊C8—22no—
660C22⋊C8—22no—
661C22⋊C8—48no—
662C22⋊C8—48no—
663C22⋊C8—48no—
664C22⋊C8—41no—
665C22⋊C8—42no—
666C22⋊C8—41no—
667C22⋊C8—42no—
668C22⋊C8—42no—
669#97—22no—
670#97—22no—
671#97—48no—
672#97—42no—
673C4×C8—41no—
674C4×C8—42no—
675C4×C8—41no—
676C4×C8—42no—
677C4×C8C4×D411yescharacteristic
678C4×C8C4×D411yescharacteristic
679C4×C8C4×D411yescharacteristic
680C4×C8C4×D411yescharacteristic
681C4×C8C4×D411yescharacteristic
682C4×C8C4×D411yescharacteristic
683C4×C8C23×C411yescharacteristic
684C4×C8C23×C411yescharacteristic
685C4×C8C23×C411yescharacteristic
686C4×C8C22×D414yes—
687C4×C8C22×D414yes—
688C4×C8C22×D411yescharacteristic
689C4×C8C22×D411yescharacteristic
690C4×C8C22×D411yescharacteristic
691C4×C8C2×#4111yescharacteristic
692C4×C8C2×#4111yescharacteristic
693C4×C8C2×#4111yescharacteristic
694C4×C8C2511yescharacteristic
695C24—41no—
696C24—42no—
697C24#44211yescharacteristic
698#41—44no—
699#41—44no—
700#41—82no—
701#41—82no—
702#41—84no—
703#41—84no—
704#41—88no—
705#41—164no—
706#41—164no—
707#41—164no—
708C2×Q8—22no—
709C2×Q8—41no—
710C2×Q8—42no—
711C2×Q8—42no—
712C2×Q8—42no—
713C2×Q8—42no—
714C2×Q8—162no—
715C2×D4—22no—
716C2×D4—24no—
717C2×D4—24no—
718C2×D4—42no—
719C2×D4—42no—
720C2×D4—44no—
721C2×D4—44no—
722C2×D4—44no—
723C2×D4—41no—
724C2×D4—42no—
725C2×D4—42no—
726C2×D4—42no—
727C2×D4—42no—
728C2×D4—42no—
729C2×D4—42no—
730C2×D4—44no—
731C2×D4—84no—
732C2×D4—162no—
733C2×D4—162no—
734C2×D4—164no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—42no—
738C22×C4—41no—
739C22×C4—41no—
740C22×C4—41no—
741C22×C4—42no—
742C22×C4—42no—
743C22×C4—42no—
744C22×C4—42no—
745C22×C4—42no—
746C22×C4—44no—
747C22×C4—42no—
748C22×C4—42no—
749C22×C4—44no—
750C22×C4—84no—
751C22×C4—81no—
752C22×C4—162no—
753C22×C4—162no—
754C22×C4—164no—
755C22×C4#44211yescharacteristic
756C22×C4#44211yescharacteristic
757C22×C4#44211yescharacteristic
758C22×C4#44211yescharacteristic
759C22×C4#44211yescharacteristic
760C22×C4#44211yescharacteristic
761C22×C4#44211yescharacteristic
762C22×C4#44211yescharacteristic
763C22×C4#44211yescharacteristic
764C22×C4C2×C4×D411yescharacteristic
765C22×C4C2×C4×D411yescharacteristic
766C22×C4C2×C4×D411yescharacteristic
767C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
768C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
769C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
770C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
771C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
772C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
773Q16—22no—
774Q16—22no—
775Q16—42no—
776SD16—44no—
777SD16—44no—
778D8—24no—
779D8—24no—
780D8—22no—
781D8—24no—
782D8—44no—
783D8—82no—
784D8—82no—
785D8C2×#13114yes—
786M16—44no—
787M16—82no—
788M16—168no—
789M16—162no—
790C2×C8—22no—
791C2×C8—22no—
792C2×C8—22no—
793C2×C8—22no—
794C2×C8—22no—
795C2×C8—21no—
796C2×C8—21no—
797C2×C8—21no—
798C2×C8—21no—
799C2×C8—24no—
800C2×C8—24no—
801C2×C8—41no—
802C2×C8—41no—
803C2×C8—41no—
804C2×C8—41no—
805C2×C8—42no—
806C2×C8—42no—
807C2×C8—44no—
808C2×C8—84no—
809C2×C8—168no—
810C2×C8—168no—
811C2×C8C2×C4×D411yescharacteristic
812C2×C8C2×C4×D411yescharacteristic
813C2×C8C2×C4×D411yescharacteristic
814C2×C8C2×C4×D411yescharacteristic
815C2×C8C2×C4×D411yescharacteristic
816C2×C8C2×C4×D411yescharacteristic
817C2×C8C2×#13112yes—
818C2×C8#56812yes—
819C2×C8C24×C411yescharacteristic
820C2×C8C22×#4111yescharacteristic
821C4⋊C4—24no—
822C4⋊C4—22no—
823C4⋊C4—22no—
824C4⋊C4—41no—
825C4⋊C4—41no—
826C4⋊C4—42no—
827C4⋊C4—42no—
828C4⋊C4—42no—
829C4⋊C4—42no—
830C4⋊C4—42no—
831C4⋊C4—42no—
832C4⋊C4—42no—
833C22⋊C4—42no—
834C22⋊C4—42no—
835C22⋊C4—42no—
836C22⋊C4—42no—
837C22⋊C4—42no—
838C22⋊C4—44no—
839C22⋊C4—44no—
840C22⋊C4—44no—
841C22⋊C4—42no—
842C22⋊C4—44no—
843C42—42no—
844C42—42no—
845C42—42no—
846C42—42no—
847C42—42no—
848C42—42no—
849C42#44211yescharacteristic
850C42#44211yescharacteristic
851C42#44211yescharacteristic
852C42#44211yescharacteristic
853C42#44211yescharacteristic
854C42#44211yescharacteristic
855C42C2×C4×D411yescharacteristic
856C42C2×C4×D411yescharacteristic
857C42C2×C4×D411yescharacteristic
858C42C2×AGL(1,ℤ/8)11yescharacteristic
859C42C2×AGL(1,ℤ/8)11yescharacteristic
860C42C2×AGL(1,ℤ/8)11yescharacteristic
861C42C2×AGL(1,ℤ/8)11yescharacteristic
862C42C2×AGL(1,ℤ/8)11yescharacteristic
863C42C2×AGL(1,ℤ/8)11yescharacteristic
864C42C23×D411yescharacteristic
865C16—24no—
866C16—24no—
867C16—24no—
868C16—42no—
869C23—22no—
870C23—41no—
871C23—41no—
872C23—42no—
873C23—44no—
874C23—44no—
875C23—84no—
876C23—161no—
877C23—161no—
878C23—162no—
879C23—162no—
880C23C2×#44211yescharacteristic
881C23C2×#44211yescharacteristic
882C23C2×#44211yescharacteristic
883Q8—42no—
884Q8—42no—
885Q8—82no—
886Q8—84no—
887Q8—162no—
888D4—24no—
889D4—42no—
890D4—44no—
891D4—44no—
892D4—44no—
893D4—84no—
894D4—84no—
895D4—84no—
896D4—88no—
897D4—84no—
898D4—84no—
899D4—162no—
900D4—162no—
901D4—164no—
902C2×C4—22no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—42no—
922C2×C4—42no—
923C2×C4—42no—
924C2×C4—44no—
925C2×C4—84no—
926C2×C4—84no—
927C2×C4—84no—
928C2×C4—88no—
929C2×C4—82no—
930C2×C4—84no—
931C2×C4—162no—
932C2×C4—162no—
933C2×C4—164no—
934C2×C4—161no—
935C2×C4—161no—
936C2×C4—162no—
937C2×C4#293312yes—
938C2×C4C2×#44211yescharacteristic
939C2×C4C2×#44211yescharacteristic
940C2×C4C2×#44211yescharacteristic
941C2×C4C2×#44211yescharacteristic
942C2×C4C2×#44211yescharacteristic
943C2×C4C2×#44211yescharacteristic
944C2×C4C2×#44211yescharacteristic
945C2×C4C2×#44211yescharacteristic
946C2×C4C2×#44211yescharacteristic
947C2×C4#295612yes—
948C2×C4C22×C4×D411yescharacteristic
949C2×C4C22×AGL(1,ℤ/8)11yescharacteristic
950C2×C4C22×AGL(1,ℤ/8)11yescharacteristic
951C8—21no—
952C8—21no—
953C8—21no—
954C8—21no—
955C8—21no—
956C8—21no—
957C8—44no—
958C8—44no—
959C8—82no—
960C8—82no—
961C8—84no—
962C8#293312yes—
963C8C22×#13111yescharacteristic
964C8C2×#56811yescharacteristic
965C22—21no—
966C22—21no—
967C22—21no—
968C22—21no—
969C22—21no—
970C22—21no—
971C22—21no—
972C22—21no—
973C22—44no—
974C22—82no—
975C22—82no—
976C22—82no—
977C22—84no—
978C22—84no—
979C22—84no—
980C22—164no—
981C22—324no—
982C22#1800112yes—
983C22C22×#44211yescharacteristic
984C4—21no—
985C4—21no—
986C4—21no—
987C4—21no—
988C4—21no—
989C4—21no—
990C4—21no—
991C4—21no—
992C4—21no—
993C4—82no—
994C4—82no—
995C4—84no—
996C4—82no—
997C4#1800112yes—
998C4#3347112yes—
999C4C2×#293311yescharacteristic
1000C4C2×#295611yescharacteristic
1001C2—22no—
1002C2—41no—
1003C2—41no—
1004C2—84no—
1005C2—164no—
1006C2C2×#1800111yescharacteristic
1007C2C2×#3347111yescharacteristic
1008C2#762263511yescharacteristic
subgroupG/H
center, socleC22C22×#442
commutatorC2×C8C24×C4
Frattini, cosocleC4×C8C25
prime radicalC2×#33675C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×C42 ◁ #17323 ◁ G
LECSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #6345152C2semidirect
3. #6345074C2semidirect
4. #484053C2semidirect
5. #484047C2semidirect
6. #483841C2semidirect
7. #483813C2semidirect
8. #483811C2semidirect
9. #483596C2semidirect
10. #483420C2semidirect
11. #481345C2semidirect
12. #481065C2semidirect
13. #479963C2semidirect
32. #18091C22semidirect
34. #18073C22semidirect
36. #18065C22semidirect
38. #18045C22semidirect
51. #12087C22semidirect
52. #12078C22semidirect
53. #12077C22semidirect
54. #12067C22semidirect
55. #12031C22semidirect
56. #12030C22semidirect
59. #11680C22semidirect
60. #11678C22semidirect
67. #11598C22semidirect
68. #11597C22semidirect
69. #11414C22semidirect
70. #11413C22semidirect
497. C2×D8#131semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#336752
#63451522
#63450742
#4840532
#4840472
#4838412
#4838132
#4838112
#4835962
#4834202
#4813452
#4810652
#4799632